Created on: September 11, 2014

Website Address: https://library.curriki.org/oer/Curriki-Calculus-Limits-and-Continuity

TABLE OF CONTENTS

- Limits and Continuity Table of Contents by Standard
- LC.1: Understand the concept of limit
- LC.2: Find limits by substitution.
- LC.3: Find limits of sums, differences, products, and quotients.
- LC.4: Find one-sided limits.
- LC.5: Find limits of rational functions that are undefined at a point.
- LC.6: Find limits at infinity.
- LC.7: Decide when a limit is infinite.
- LC.8: Understand continuity in terms of limits.
- LC.9: Decide if a function is continuous at a point.
- LC.10: Find the types of discontinuities of a function.
- LC.11: Understand and use the Intermediate Value Theorem
- LC.12: Understand and apply the Extreme Value Theorem

In this, the first of the five major categories of this course, the topics covered include:

Limits of functions (including one-sided limits)

• An intuitive understanding of the limiting process.

• Calculating limits using algebra.

• Estimating limits from graphs or tables of data.

Asymptotic and unbounded behavior

• Understanding asymptotes in terms of graphical behavior.

• Describing asymptotic behavior in terms of limits involving infinity.

• Comparing relative magnitudes of functions and their rates of change (for example,

contrasting exponential growth, polynomial growth, and logarithmic growth).

Continuity as a property of functions

• An intuitive understanding of continuity. (The function values can be made as

close as desired by taking sufficiently close values of the domain.)

• Understanding continuity in terms of limits.

• Geometric understanding of graphs of continuous functions (Intermediate

Value Theorem and Extreme Value Theorem).

Resources in this section listed by standard.

Understand the concept of limit and estimate limits from graphs and tables of values.

Find limits by direct substitution.

Find limits of sums, differences, products, and quotients.

Find one-sided limits.

Find limits of rational functions that are undefined at a point.

Find limits at positive or negative infinity.

Decide when a limit is infinite and use limits involving infinity to describe asymptotic behavior.

Understand continuity in terms of limits and functional values.

Decide if a function is continuous at a point using definition of continuity.

Find the types of discontinuities of a function: Removable, Infinite, Jump.

Understand and use the Intermediate Value Theorem on a function over a closed interval.

Understand and apply the Extreme Value Theorem: If f is continuous over a closed interval, then f has a maximum and a minimum on the interval.